Disorder Induced Localized States in Graphene

TL;DR

This paper investigates how vacancies in graphene create localized electronic states, which become resonances when particle-hole symmetry is broken, and explores the effects of disorder on electronic localization.

Contribution

It provides a detailed analysis of vacancy-induced localized states in graphene and their evolution with broken symmetry, extending to disordered systems and related superconductors.

Findings

Vacancies induce localized states in graphene.

Broken particle-hole symmetry turns these into resonances.

Disorder affects electronic density of states and localization.

Abstract

We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is shown that vacancies induce the formation of localized states. When particle-hole symmetry is broken, localized states become resonances close to the Fermi level. We also study the problem of a finite density of vacancies, obtaining the electronic density of states, and discussing the issue of electronic localization in these systems. Our results also have relevance for the problem of disorder in d-wave superconductors.